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Most of the 60 moons in the Saturn system are far away from the rings and very small, so their effect on the rings is negligible. But larger ones that are closer in (Enceladus) do have a rather significant effect on the rings, but as the gravitational pull of these moons is radially outward, it is hardly visible. On the other hand, small moons inside the ...


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I think what you have established here is just that $\rho$ tends to increase with mass. The density of planets isn't constant. Let $\rho = \rho_0 (M/M_{earth})^{\alpha}$, so that $M = (4/3)\pi R^{3} \rho_0 (M/M_{earth})^{\alpha}$ Then $$g = \frac{GM}{R^2} = \frac{4\pi G}{3} R \rho$$ Replace $R$ with $(3M/4\pi \rho)^{1/3}$ so that $$ g = \frac{4\pi G}{3} ...


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For planets of constant mean density you have: $$ M=\rho \times 4\pi r^3 $$ and the surface value of $g$ is: $$ g(r)=\frac{GM}{r^2}=G \times \rho\times 4 \pi \times r $$ So for bodies of constant density the surface gravity is proportional to the radius, and the slope as $r \to 0$ tells you the density. So for bodies of equal density $\log(g(r)) \to -\infty$ ...



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